The No.1-seeded Williams wasn't thrilled with her performance - after all, she has only had two days to switch from the hardcourts of Miami to the clay courts of Charleston - but she was sharp anyway, firing nine aces to zero double faults and breaking serve five times to get by the crafty Giorgi, 62 63.
"It definitely wasn't great for me - I played well, but I wasn't great, footing-wise," Williams said. "I was just trying to get my stability. I only had one or two days of practice. But I felt good - I'm glad I came here and hope I can get ready for what can hopefully be another good clay court season."
Williams had been keeping an eye on her opponent. "I've been watching her," she said. "I've played her in doubles before and I think she's a good player. I also saw she did really well at Wimbledon - I knew one day I would play against her, so I kind of knew how she would play going into the match."
Williams has now won 67 of her last 71 matches, a stretch that started at this event last year.
Other seeds in second round matches had mixed results, with No.11 seed Sorana Cirstea and No.12 seed Varvara Lepchenko moving on but No.7 seed Carla Suárez Navarro and No.8 seed Mona Barthel falling - Suárez Navarro lost to Stefanie Voegele in her first match as a Top 20 player, 62 64, while Barthel missed four set points in the first set and lost to American qualifier Jessica Pegula, 76(4) 61.
The 19-year-old Pegula had gotten a lot of practice on the green clay going into her match with Barthel. Not only had she battled through the qualifying and won a lengthy first round match against Garbiñe Muguruza, during which she saved match point, but she also grew up in nearby Hilton Head.
"It's an advantage, especially when she had a first round bye and everyone has been on hardcourt," Pegula said. "Every once in a while a lot of these girls are qualifying and then doing well, and they'll probably keep doing well because they have had a couple matches on the stuff. It really helps."
Pegula's wins over Muguruza and Barthel are the first two WTA main draw-level wins of her career.
"I feel like I played very well," Mattek-Sands said. "Sloane is a tough competitor. She has a lot of confidence this year. She's a great player - and on top of that I lost to her twice last year, so it was a little bit of a revenge match for me. I really wanted to stick to my game plan regardless of how she was going to play - I wanted to play aggressive and make it shorter than yesterday, win or lose.
"Every single point I was going to be aggressive and I focused on every single point."
"She has this game I don't really like and doesn't really suit me - I always have trouble with her," Jankovic said. "But actually it was our first time playing on clay and the other two times we played on grass, so it was a different surface this time. Overall I think I played a pretty good match today."
"Whenever we play we always have tough matches," Oudin said. "Some people play better against a certain kind of game. I feel like normally whenever I play her, even today, it's a good match. I was definitely disappointed I didn't win, but I think this was the best match I've played so far this year."
Lisicki defeated Anna Tatishvili, 60 60, the German's first such scoreline at the WTA level.
"Especially since we don't have that much time switching from hard to clay, it's always great when you play so well in the first round," said Lisicki, who won the Family Circle Cup in 2009. "I've played well at this event before and I enjoy being here. I always play better once I step on that center court."